Answer:
Step-by-step explanation:
You just need the distance formula here. It's very simple to follow:
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
which, for us, looks like this:
[tex]d=\sqrt{(13-4)^2+(19-7)^2}[/tex] and
[tex]d=\sqrt{9^2+12^2}[/tex] and
[tex]d=\sqrt{81+144}[/tex] and
[tex]d=\sqrt{225}[/tex] so
d = 15
Describe your research question, and explain its importance. Describe how you would use the four-step hypothesis test process to answer your research question. Explain how using a t test could help you answer your research question.
Answer:
See explanation below
Step-by-step explanation:
Data given and notation
First we need to find the sample mean and deviation from the data with the following formulas:
[tex]\bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
[tex]\bar X[/tex] represent the sample mean
[tex]s[/tex] represent the sample standard deviation
[tex]n[/tex] sample size
[tex]\mu_o [/tex] represent the value that we want to test
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We have three possible options for the null and the alternative hypothesis:
Case Bilateral
Null hypothesis:[tex]\mu = \mu_o[/tex]
Alternative hypothesis:[tex]\mu \neq \mu_o[/tex]
Case Right tailed
Null hypothesis:[tex]\mu \leq \mu_o[/tex]
Alternative hypothesis:[tex]\mu > \mu_o[/tex]
Case Left tailed
Null hypothesis:[tex]\mu \geq \mu_o[/tex]
Alternative hypothesis:[tex]\mu < \mu_o[/tex]
We assume that w don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) and the value obtained is assumed as [tex]t_o[/tex]
Calculate the P-value
First we need to find the degrees of freedom:
[tex] df=n-1[/tex]
Case two tailed
Since is a two-sided tailed test the p value would be:
[tex]p_v =2*P(t_{df}>|t_o|)[/tex]
Case Right tailed
Since is a one-side right tailed test the p value would be:
[tex]p_v =P(t_{df}>t_o)[/tex]
Case Left tailed
Since is a one-side left tailed test the p value would be:
[tex]p_v =P(t_{df}<t_o)[/tex]
Conclusion
The rule of decision is this one:
[tex]p_v >\alpha[/tex] We fail to reject the null hypothesis at the significance level [tex]\alpha[/tex] assumed
[tex]p_v <\alpha[/tex] We reject the null hypothesis at the significance level [tex]\alpha[/tex] assumed
A boat whose speed in 15km/hr in still water goes 30 km downstream and come back in a total of 4 hours 30 minutes.The speed of the stream(in km/hr) is
Answer: total Distance = 60km
Time = 4.5hrs
Speed = 60/4.5
13⅓km/hr
Step-by-step explanation:
1) Which equations represent functions that are non-linear? Select each correct answer.
a) Y = X
b) 2Y= 4x+6
c ) Y = 8 + x
d) Y - 6 = x^2
e) Y= - 3x+l/5
f) Y=2x^2+5-3x^2
Answer:
d) Y - 6 = x²; f) Y = 2x² + 5 - 3x²
Step-by-step explanation:
Functions in which the exponent of x is not equal to one are nonlinear.
Functions in which the exponent of x is equal to one are linear.
Tyrone’s financial goal is to create an emergency fund. To make Tyrone’s financial goal specific, he could give himself a . To make his goal timely, he could give himself a .
Answer:
Goal amount of $10,000
Deadline of next year
Step-by-step explanation:
Tyrone can make his financial goal ‘specific’ by deciding on a target amount for his emergency fund. He can make it 'timely' by assigning a deadline by which to save that amount.
Explanation:To make Tyrone's financial goal specific, he could give himself a target amount to save for the emergency fund. This could be a fixed sum, like $1000, or a figure based on monthly expenses, like saving for 6 months' worth of living expenses. This clarity can help him to plan and track his progress.
To make his goal timely, he could give himself a deadline by which he wants to achieve this goal. For example, he might aim to save his specified amount within a year or two. The timetable can provide added motivation to adhere to a budget and save consistently.
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A Lights-A-Lot quality inspector examines a sample of 25 strings of lights and finds that 6 are defective. What is the experimental probability that a string of lights is defective?
Final answer:
The experimental probability of a string of lights being defective is calculated by dividing the number of defective strings found during the inspection by the total number of strings inspected, leading to a probability of 6/25.
Explanation:
The experimental probability that a string of lights is defective is determined by dividing the number of defective strings of lights by the total number of strings inspected. This probability can be calculated as follows:
Number of defective strings = 6
Total number of strings inspected = 25
Experimental Probability = Number of defective strings / Total number of strings
So, the experimental probability of finding a defective string of lights is 6/25.
By [n][n] we denote the set {1,…,n}. A function f:[m]→[n] is called monotone if f(i) \leq f(j)f(i)≤f(j)whenever i < ji
Answer:
There are a total of [tex] { 6 \choose 3} = 20 [/tex] functions.
Step-by-step explanation:
In order to define an injective monotone function from [3] to [6] we need to select 3 different values fromm {1,2,3,4,5,6} and assign the smallest one of them to 1, asign the intermediate value to 2 and the largest value to 3. That way the function is monotone and it satisfies what the problem asks.
The total way of selecting injective monotone functions is, therefore, the total amount of ways to pick 3 elements from a set of 6. That number is the combinatorial number of 6 with 3, in other words
[tex] {6 \choose 3} = \frac{6!}{3!(6-3)!} = \frac{720}{6*6} = \frac{720}{36} = 20 [/tex]
Question 3 (1 point)
What is the midpoint of E (9, 7) and F (-1, 5)?
Question 3 options:
(4, 6)
(10, 2)
(5, 1)
(8, 12)
Answer:
The answer to your question is (4, 6)
Step-by-step explanation:
Data
E ( 9 , 7 )
F ( - 1, 5)
Formula
[tex]Xm = \frac{x1 + x2}{2}[/tex]
[tex]Ym = \frac{y1 + y2}{2}[/tex]
Substitution and simplification
[tex]Xm = \frac{9 -1}{2}[/tex]
[tex]Xm = \frac{8}{2}[/tex]
Xm = 4
[tex]Ym = \frac{7 + 5}{2}[/tex]
[tex]Ym = \frac{12}{2}[/tex]
Ym = 6
Result
(4 , 6)
please help
with my geomtry homework
Answer:
Therefore, HL theorem we will prove for Triangles Congruent.
Step-by-step explanation:
Given:
Label the Figure first, Such that
Angle ADB = 90 degrees,
angle ADC = 90 degrees, and
AB ≅ AC
To Prove:
ΔABD ≅ ΔACD by Hypotenuse Leg theorem
Proof:
In Δ ABD and Δ ACD
AB ≅ AC ……….{Hypotenuse are equal Given}
∠ADB ≅ ∠ADC ……….{Each angle measure is 90° given}
AD ≅ AD ……….{Reflexive Property or Common side}
Δ ABD ≅ Δ ACD ….{By Hypotenuse Leg test} ......Proved
Therefore, HL theorem we will prove for Triangles Congruent.
Yuan receives money from his relatives every year on his birthday. This year, Yuan received a total of $56. That is 12% more than he received last year. How much did Yuan received last year?
Answer:Yuan received $50 last year
Step-by-step explanation:
Yuan receives money from his relatives every year on his birthday.
Let x represent the amount of money that Yuan received last year on his birthday.
This year, Yuan received a total of $56. The amount that he received this year is 12% more than he received last year. This means that
the increment on the amount that he received last year is would be
12/100×x = 0.12x. Therefore,
x + 0.12x = 56
1.12x = 56
x = 56/1.12 = $50
What are the factors of the polynomial function?
Good evening ,
Answer:
(x-1) ; (x+3) and (x+5).
Step-by-step explanation:
Since 1 , -3 , -5 are roots of the polynomial function
then the factors of f are:
(x-1) ; (x+3) and (x+5).
:)
Which of the following statements shows the distributive property?
5 + (4 – 2) = 20 – 10
5(4 – 2) = 20 – 10
5 + (4 – 2) = 9 + 3
5(4 – 2) = 9 – 7
Answer:
[tex]\displaystyle 5(4 - 2) = 20 - 10[/tex]
This is a genuine statement of you look real closely at it.
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The distributive property is demonstrated in the equation 5(4 - 2) = 20 - 10, where multiplication outside the parentheses is distributed to each term within the parentheses.
The distributive property in mathematics is an algebraic property used to multiply a single term and two or more terms inside a set of parentheses. The correct statement that shows the distributive property among the given options is: 5(4 - 2) = 20 - 10.
Applying the distributive property, we would multiply the 5 by each term inside the parentheses: 5 * 4 = 20 and 5 * (-2) = -10. Hence, we have 5 * 4 - 5 * 2 = 20 - 10, which is a correct demonstration of this property.
To better understand, let me explain it step-by-step:
Multiply the term outside the parenthesis (5) by each of the terms inside the parenthesis (4 and -2).
Perform the multiplication: 5 * 4 = 20 and 5 * (-2) = -10
Combine the results to show that 5(4 - 2) is indeed equal to 20 - 10.
Mindy divides a rectangular piece of fabric into a equal-sized pieces for to suing projects for project a she will need she will use 1/2 of the fabric for Project B she will use 1/4 of the fabric draw a model to show how the fabric was divided and which piece will be used what unit fraction represents one of the pieces write an equation to find how much of the fabric will not be used let F represent the fraction of leftover fabric what is the answer?
Answer:F=A-(A/2+A/4)
=> F=1/4
Step-by-step explanation:
Let A represent the initial quality of rectangular fabric.
Half of A was used for the sewing project
Quarter of the left over was used for project B
Hence a quarter of unused fabric(F) will be left.
In a student government election, 7,000 students cast a vote for the incumbent, 900 vote for the opponent, and 100 cast a protest vote. What was the ratio of the incumbent”s votes in the total number of votes?
-Jarvis
Answer:
The ratio of the incumbent”s votes in the total number of votes = 7:8
Step-by-step explanation:
Given:
Number of students who cast vote for the incumbent = 7,000
Number of students who cast vote for the opponent = 900
Number of protest votes = 100
To find ratio of the incumbent”s votes in the total number of votes.
Solution:
Total number of votes cast = [tex]7000+900+100=8000[/tex]
Number of votes for incumbent = [tex]7000[/tex]
Ratio of incumbent”s votes in the total number of votes can be calculated as:
⇒ [tex]\frac{\textrm{The incumbent's votes}}{\textrm{Total number of votes}}[/tex]
⇒ [tex]\frac{7000}{8000}[/tex]
Simplifying to simplest fraction by dividing numerator and denominator by 1000.
⇒ [tex]\frac{7000\div1000}{8000\div1000}[/tex]
⇒ [tex]\frac{7}{8}[/tex]
Thus, ratio of the incumbent”s votes in the total number of votes = 7:8
What is the average rate of change of the function
f(x)=480(0.3)x from x = 1 to x = 5?
Enter your answer, as a decimal, in the box.
Do not round your answer.
Answer:
Average rate of change [tex]=-35.7084[/tex]
Step-by-step explanation:
Given function is [tex]f(x)=480(0.3)^x[/tex] and we need to find average rate of change of the function from [tex]x=1\ to\ x=5[/tex].
Average rate of change [tex]=\frac{f(b)-f(a)}{b-a}[/tex]
So,
[tex]here\ b=5\ and\ a=1\\f(5)=480(0.3)^5\\=480\times0.00243=1.1664\\and\\f(1)=480(0.3)^1\\=480\times0.3=144[/tex]
Average rate of change
[tex]=\frac{f(b)-f(a)}{b-a}\\\\=\frac{f(5)-f(1)}{5-1}\\\\=\frac{1.1664-144}{5-1}\\\\=\frac{-142.8336}{4}= -35.7084[/tex]
Hence, average rate of change of the function [tex]f(x)=480(0.3)^x[/tex] over the intervel [tex]x=1\ to\ x=5[/tex] is [tex]=-35.7084[/tex].
Answer:
-35.8074 is the correct answer
Step-by-step explanation:
A hardware store rents vacuum cleaners that customers may use for part or all of a day, before returning. The store charges a flat fee plus an hourly rate. Choose the linear function f for the total rental cost of a vacuum cleaner.
In the context of renting a vacuum cleaner for an hourly rate plus a flat fee from a hardware store, the total rental cost can be represented as a linear function. If we consider the flat fee to be $31.50 and the hourly rate to be $32, the function would be f(x) = 31.50 + 32x, where x is the rental duration in hours.
Explanation:The question pertains to a linear function, which is a fundamental concept in algebra and represents a straight line when graphed. Such a function is typically expressed in the form y = mx + b, where m and b are constants, y is the dependent variable, and x is the independent variable.
In the context of the question, the total rental cost for a vacuum cleaner from the hardware store can be a linear function if it involves both a fixed cost (the flat fee) and an hourly rate charge. Specifically, the flat fee can be represented as the constant b, which will be added to regardless of the number of hours the vacuum cleaner has been rented.
On the other hand, the hourly rate charge is the variable cost that alters in relation to the rental duration and can be shown as m times x. Thus, if we consider the flat fee to be $31.50 and the hourly rate to be $32 (as in the reference), the total rental cost function, f, can be formulated as follows: f(x) = 31.50 + 32x
In this equation, x stands for the number of hours the vacuum cleaner is rented. Consequently, by substituting the rental duration into the equation, it would be feasible to compute the total rental cost.
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9. 10. To solve 2x x 2 11 x = 8 x 2 2x , Ren multiplied both sides by the least common denominator. Which statement is true? A. 2 is an extraneous solution. B. 7 2 is an extraneous solution. C. 0 and 2 are extraneous solutions. D. This equation does not contain any extraneou
Answer:
2 is the extraneous solution
Step-by-step explanation:
Given equation is
[tex]\frac{2x}{x-2} -\frac{11}{x} =\frac{8}{x^2-2x}[/tex]
Factor the denominator
[tex]\frac{2x}{x-2} -\frac{11}{x} =\frac{8}{x(x-2)}[/tex]
LCD is x(x-2), multiply all the fractions by LCD
[tex]2x \cdot x-11(x-2)=8[/tex]
[tex]2x^2-11x+22= 8[/tex], subtract 8 from both sides
[tex]2x^2-11x+14=0[/tex]
factor the left hand side
[tex]2x^2-7x-4x+14= 0[/tex]
[tex]x(2x-7)-2(2x-7)=0[/tex]
[tex](x-2)(2x-7)=0[/tex]
x-2=0, so x=2
2x-7=0, [tex]x=\frac{7}{2}[/tex]
when x=2, then the denominator becomes 0 that is undefined
So 2 is the extraneous solution
The question is asking which statement is true regarding the potential extraneous solutions after solving an algebraic equation by multiplying both sides by the least common denominator. To determine if a solution is extraneous, it must be checked against the original equation. Without the specific manipulations made by Ren, we cannot assess the given options.
Explanation:To solve the equation 2x x 2 11 x = 8 x 2 2x, Ren multiplied both sides by the least common denominator to eliminate the fractions and then used algebraic techniques to find the solutions for x. We know that when we have an equation of the form (ax + b)x = 0, there are two multiplicands, and we can set each equal to zero to solve for x. This leads to two solutions.
After solving, we need to check each solution by substituting it back into the original equation to confirm whether or not the solution is extraneous. An extraneous solution is one that does not satisfy the original equation after simplification. Checking is important as it ensures that the proposed solutions indeed make the original equation an identity, such as 6 = 6.
Without the specific equation after Ren's manipulations, we cannot evaluate the statements A, B, C, or D directly. However, we can understand that extraneous solutions arise when certain steps in solving an equation (like squaring both sides or multiplying by a variable expression) introduce results that are not true for the original equation.
Shear strength measurements for spot welds have been found to have standard deviation 1 0 pounds per square inch (psi). If 100 test welds are to be measured, what is the approximate probability that the sample mean will be within 1 psi of the true population mean.
Answer:
[tex]P(\mu -1< \bar X <\mu +1)=0.6826[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Let X the random variable that represent the Shear strength of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(\mu,10)[/tex]
Where [tex]\mu[/tex] and [tex]\sigma=10[/tex]
And let [tex]\bar X[/tex] represent the sample mean, the distribution for the sample mean is given by:
[tex]\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})[/tex]
On this case [tex]\bar X \sim N(\mu,\frac{10}{\sqrt{100}})[/tex]
We are interested on this probability
[tex]P(\mu -1<\bar X<\mu +1)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
If we apply this formula to our probability we got this:
[tex]P(\mu -1<\bar X<\mu +1)=P(\frac{\mu- 1-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{X-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{\mu +1-\mu}{\frac{\sigma}{\sqrt{n}}})[/tex]
[tex]=P(\frac{\mu -1-\mu}{\frac{10}{\sqrt{100}}}<Z<\frac{\mu +1-\mu}{\frac{10}{\sqrt{100}}})=P(-1<Z<1)[/tex]
And we can find this probability on this way:
[tex]P(-1<Z<1)=P(Z<1)-P(Z<-1)[/tex]
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
[tex]P(-1<Z<1)=P(Z<1)-P(Z<-1)=0.8413-0.1587=0.6826[/tex]
The probability that the sample mean will be within 1 psi of the true population mean is approximately 68.2%, according to the properties of a normal distribution and the central limit theorem.
Explanation:This is a problem of standard deviation and probability in relation to the sample mean. This type of problem can be solved by knowing the properties of a normal distribution.
The central limit theorem states that if we have a large enough sample, the distribution of the sample mean will approximate a normal distribution regardless of the distribution of the population.
For this scenario, where the true population mean is unknown, the standard deviation of the sampling distribution (also known as the standard error) can be calculated as the original standard deviation (10 psi) divided by the square root of the sample size (100 test welds in this case), hence 10 ÷ √100 = 1 psi.
Then, to find the probability that the sample mean is within 1 psi of the true population mean, we can refer to the Z-table (a standard normal distribution table) to find the corresponding probability for z = ±1 (because the z-score for ±1 standard error from the mean is ±1). This value is approximately 68.2%
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Assume that a procedure yields a binomial distribution with a trial that is repeated 10 times. Use the binomial probability formula to find the probability of 6 successes given that a single success has a probability of 0.30.
Answer: 0.036756909
Step-by-step explanation:
Formula for Binomial probability distribution.
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex]
, where x= number of success
n= total trials
p=probability of getting success in each trial.
According to the given information , we have
n= 10 , p= 0.30 and x= 6
Then, the required probability will be :
[tex]P(x=6)=^{10}C_6(0.3)^6(1-0.3)^{10-6}\\\\= \dfrac{10!}{6!(10-6)!}\times(0.3)^6(0.7)^4\\\\=\dfrac{10\times9\times8\times7\times6!}{6!4!}(0.3)^6(0.7)^4\\\\=(210)(0.000729)(0.2401)=0.036756909[/tex]
Hence, the required provability = 0.036756909
The probability of 6 successes given that a single success has a probability of 0.30 is given by the binomial distribution and P ( A ) = 0.03675 or 3.675 %
Given data ,
To find the probability of exactly 6 successes in 10 trials, with a probability of success (p) equal to 0.30, we can use the binomial probability formula:
P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ
P(X = k) is the probability of getting exactly k successes,
n is the total number of trials,
k is the number of desired successes,
p is the probability of success for a single trial,
In this case, n = 10, k = 6, and p = 0.30. The binomial coefficient C(n, k) is calculated as:
P(n, k) = n! / (k! * (n - k)!)
Substituting the values into the formula, we have:
P(X = 6) = C(10, 6) x (0.30)⁶ * (1 - 0.30)⁽¹⁰⁻⁶⁾
Calculating the binomial coefficient:
C(10, 6) = 10! / (6! x (10 - 6)!)
= 10! / (6! x 4!)
= (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1)
= 210
Substituting the values into the formula:
P(X = 6) = 210 x (0.30)⁶ (0.70)⁴
P ( X = 6 ) = P ( A ) = 210 ( 0.000729 ) ( 0.2401 )
P ( A ) = 0.036756909
Therefore, the probability of getting exactly 6 successes in 10 trials, with a probability of success of 0.30, is approximately 0.03675 or 3.675 %
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Can someone please explain how to do this?? I got the wrong answer and I don't know how to do this question
Find the area of the triangle with a = 19, b = 14, c = 19. Round to the nearest tenth.
thank you
Answer:
[tex]\displaystyle 133\:square\:units[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{1}{2}hb = A, \frac{1}{2}bh = A, or\: \frac{hb}{2} = A[/tex]
For the two legs, no matter what you do, you can either take half of 19 [9½] and multiply it by 14, take half of 14 [7] and multiply it by 19, or you could multiply both 14 and 19 [266] then take of that.
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slader An electronics company is planning to introduce a new camera phone. The company commissions a marketing report for each new product that predicts either the success or failure of the product. Of new products introduced by the company, 60% have been successes. Furthermore, 70% of their successful products were predicted top be successes, while 40% of failed products were predicted to be successes. Find the probability that this new camera phone will be successful if its success has been predicted.
Answer: Our required probability is 0.7241.
Step-by-step explanation:
Since we have given that
Probability that new product have been successes P(S) = 60%
Probability that new product have not been successes P(F) = 40%
Probability that their successful products were predicted to be successes = P(A|S)=70%
Probability that their failed products were predicted to be successes =P(A|F) = 40%
So, Probability that this new camera phone will be successful if its success has been predicted is given by
[tex]P(S|A)=\dfrac{P(S).P(A|S)}{P(S).P(A|S)+P(F).P(A|F)}\\\\P(S|A)=\dfrac{0.7\times 0.6}{0.7\times 0.6+0.4\times 0.4}\\\\P(S|A)=0.7241[/tex]
Hence, our required probability is 0.7241.
The end points of a diameter of a circle are (6,2) and (-4,7).
What is the standard form of the equation
Enter any fraction is simplified form
Answer:
Step-by-step explanation:
The standard form equation of a circle with radius r is expressed as
( x − h )^2 + ( y − k )^2 =r ^2 ,
where r represents the radius
h and k are the coordinates of the center of the circle C( h , k )
To determine the coordinates at the center of the circle, the midpoint formula would be used. It is expressed as
[(x1 + x2)/2 , (y1 + y2)/2]
Midpoint of the circle =
(6 - 4)/2 , (2 + 7)/2 = (1, 4.5)
h coordinate of the center = 1
k coordinate of the center = 4.5
r^2 = (x - h)^2 + (2 - k)^2
r^2 = (6 - 1)^2 + (2 - 4.5)^2
r^2 = 5^2 + (- 2.5)^2 = 25 + 6.25
r^2 = 31.25
Substituting r^2 = 31.25, h = 1 and k = 4.5 into (x − h )^2 + ( y − k )^2 = r^2, the standard equation of the circle becomes
(x − 1 )^2 + ( y − 4.5 )^2 = 31.25
Final answer:
The standard form of the equation is (x - 1)² + (y - 4.5)² = 31.25.
Explanation:
The student is asking for the standard form equation of a circle given the endpoints of a diameter. To find the center of the circle, we average the x-coordinates and the y-coordinates of the endpoints, resulting in the center coordinates (1, 4.5).
The radius can be calculated using the distance formula between the center and one of the endpoints, which gives us √((6-1)²+(2-4.5)²) = √(5²+2.5²) = √(25+6.25) = √31.25.
The radius in its simple form is √31.25.
The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Substituting the values we have, the equation becomes (x - 1)² + (y - 4.5)² = (√31.25)², which simplifies to
(x - 1)² + (y - 4.5)² = 31.25.
There are 81 pencils in a box. Abigail removes 5 pencils, Barry removes 2 pencils, Cathy removes 6 pencils and David adds 5 pencils to the box. How many pencils are left in the box?
Answer:
73 pencils
Step-by-step explanation:
There are 81 pencils in a box.
Abigail removes 5 pencils, thus we have 81-5 = 76 left
Barry removes 2 pencils, it becomes 76-2 = 74
Cathy removes 6 pencils, now it is 74-6= 68
and David adds 5 pencils to the box,
Now we have 68+5=73 pencils left in the box.
Three different die are rolled __ probability that exactly to roll tthe same number.
Answer: Our required probability is [tex]\dfrac{1}{36}[/tex]
Step-by-step explanation:
Since we have given that
Total number of outcomes in single die = 6
So, total number of outcomes if three different die = [tex]6^3=216[/tex]
Number of favourable outcome i.e. exactly roll the same number = (1,1,1), (2,2,2) (3,3,3) (4,4,4) (5,5,5), (6,6,6) = 6
So, Probability of getting exactly roll the same number is given by
[tex]\dfrac{\text{number of favourable outcome}}{\text{Number of total outcomes}}\\\\=\dfrac{6}{216}\\\\=\dfrac{1}{36}[/tex]
Hence, our required probability is [tex]\dfrac{1}{36}[/tex]
Luis hizo un viaje en el coche en el cual consumio 20 l de gasolina. el trayecto lo hizo en dos etapas en la primera consumio 2/3 de la gasolina que tenia en el deposito y en la segunda, la mitadque le quedaba. ¿cuanta gasolina habia en el deposito?
Answer: [tex]24\ liters[/tex]
Step-by-step explanation:
Let be "x" the amount of gasoline in liters that the car's tank had at the beginning of the trip.
1. In the first part of the trip the amount of gasoline the car used can be expressed as:
[tex]\frac{2}{3}x[/tex]
2. After the first part of the trip, the remaining was:
[tex]x-\frac{2}{3}x=\frac{1}{3}x[/tex]
3. In the second part of the trip the car used [tex]\frac{1}{2}[/tex] of the remaining. This is:
[tex](\frac{1}{3}x)(\frac{1}{2})=\frac{1}{6}x[/tex]
4. The total amount ot gasoline used in this trip was 20 liters.
5. Then, with this information, you can write the following equation:
[tex]\frac{2}{3}x+\frac{1}{6}x=20[/tex]
6. Finally, you must solve for "x" in order to find its value. This is:
[tex]\frac{2}{3}x+\frac{1}{6}x=20\\\\\frac{5}{6}x=20\\\\5x=120\\\\x=24[/tex]
List K consists of seven numbers. Is the average (arithmetic mean) of the seven numbers negative?
1) Four of the seven numbers in list K are negative.
2) The sum of the seven numbers in list K is negative.
Answer:
Yes, the average (arithmetic mean) of the seven numbers would be negative.
Step-by-step explanation:
We have been given that list K consists of seven numbers. We have been given two cases about list K. We are asked to determine whether the average (arithmetic mean) of the seven numbers negative.
1st case: Four of the seven numbers in list K are negative.
For 1st case, if the sum of 3 positive numbers is greater than sum of four negative numbers, then the average would be positive.
2nd case: The sum of the seven numbers in list K is negative.
We know that average of a data set is sum of all data points of data set divided by number of data points.
Since we have been given that sum of the seven numbers in list K is negative, so a negative number divided by any positive number (in this case 7) would be negative.
Therefore, the average (arithmetic mean) of the seven numbers would be negative.
If the sum of two positive integers is 24 and the difference of their squares is 48, what is the product of the two integers?(A) 108(B) 119(C) 128(D) 135(E) 143
Answer:
143
Step-by-step explanation:
Denote by x and y such integers. The hypotheses given can be written as:
[tex]x+y=24, x^2-y^2=48[/tex]
Use the difference of squares factorization to solve for x-y
[tex]48=x^2-y^2=(x-y)(x+y)=24(x-y)\text{ then }x-y=2[/tex]
Remember that
[tex](x+y)^2=x^2+2xy+y^2[/tex]
[tex](x-y)^2=x^2-2xy+y^2[/tex]
Substract the second equation from the first to obtain
[tex](x+y)^2-(x-y)^2=4xy[/tex]
Substituting the known values, we get
[tex]4xy=24^2-2^2=572\text{ then }xy=\frac{572}{4}=143[/tex]
The sum of the two integers is 24, and the difference of their squares is 48. By setting up a system of equations, we find the integers are 13 and 11. The product of these integers is 143.
Explanation:We are given the sum of two positive integers is 24 and the difference of their squares is 48. Let's denote the integers as x and y, with x being the larger integer. So, we have:
x + y = 24 (Equation 1)x^2 - y^2 = 48 (Equation 2)We can factor Equation 2, which is a difference of squares, into (x + y)(x - y) = 48. Using the fact that x + y = 24 (from Equation 1), we can substitute into this to get 24(x - y) = 48, which simplifies to x - y = 2. Now we have a system of equations:
x + y = 24x - y = 2Adding these two equations, we get 2x = 26, so x = 13. Subtracting the second equation from the first, we get 2y = 22, so y = 11. Now to find the product of the two integers, we multiply x and y together: 13 * 11 = 143.
Therefore, the product of the two integers is 143.
It takes 313131 employees and \$7500$7500dollar sign, 7500 to build a car, and it takes 191919 employees and \$4300$4300dollar sign, 4300 to build a motorcycle. Genghis Motors wants to spend more than \$84000$84000dollar sign, 84000 to build cars and motorbikes using at most 706706706 employees. Let CCC denote the number of cars they build and MMM the number of motorbikes they build. Write an inequality that represents the condition based on the number of employees. Write an inequality that represents the condition based on the number of dollars.
Answer:
a) 31c + 19m ≤ 706
b) 7500c + 4300m > 84000
Step-by-step explanation:
To build a car, we need 31 employees and $7500.
To build a motorcycle, we need 19 employees and $4300.
Let C denote the number of cars they build.
Let M denote the number of motorbikes they build.
Recall that ;
To build a career, we need 31 employees. To build "c" cars, we will need 31*c = 31c employees
To build a motorcycle, we need 19 employees. To build "m" motorcycle, we will need 19*m = 19m
Since the maximum number of employees used to build the car and motorcycle is at most 706, we have
31c + 19m ≤ 706
It takes $7500 to build car. To build "c" cars, we need 7500*c = $7500c
It also takes $4300 to build "m" motorcycles. We need 4300*m = $4300m
Since Genghis motors wont to spend more than $84000 on both cars and motorcycles, we have
7500c + 4300m > 84000
For the condition based on the number of employees, we have
31c + 19m ≤ 706
For the condition based on the number of dollars, we have
7500c + 4300m > 84000
Answer:
31c + 19m ≤ 706 and 7500c + 4300m > 84000
Step-by-step explanation:
In triangle ABC, the measure of angle B is 60 more than A. The measure of angle C is eight times the measure of A. If x represents the measure of angle A, set up and solve an equation to find the measure of angle A.
Answer: the measure of angle A is 12 degrees
Step-by-step explanation:
Let x represent the measure of angle A.
Let y represent the measure of angle B.
Let z represent the measure of angle C.
In triangle ABC, the measure of angle B is 60 more than A. This means that
y = x + 60
The measure of angle C is eight times the measure of A. This means that
z = 8x
Also, the sum of the angles in a triangle is 180 degrees. Therefore
x + y + z = 180 - - - - - - - - - 1
Substituting y = x + 60 and z = 8x into equation 1, it becomes
x + x + 60 + 8x = 180
10x + 60 = 180
10x = 180 - 60 = 120
x = 120/10 = 12
Answer:
Step-by-step explanation:
measure of A=x
∠C=8x
∠B=x+60
in a triangle sum of angles=180°
x+8x+x+60=180
10x=120
x=12
m∠A=12°
You want to invest in a hot dog stand near the ballpark. You have a 0.35 probability that you can turn your current $15,000 into $50,000 and an 0.65 probability that fierce competition will drive you to ruin, losing all your money. If you decide not to enter, you keep your $15,000. Would you enter the market?
Answer:
Step-by-step explanation:
The probability that you can turn your current $15,000 into $50,000. This means that the probability of success is 0.35. In terms of percentage, it is 0.35×100 = 35%
You have a 0.65 probability that fierce competition will drive you to ruin, losing all your money. This means that the probability of failure is 0.65. In terms if percentage, it is 0.65×100 = 65%
Looking at the percentage, entering the market will be too risky so I won't enter market since the chance of failing is very high compared to that of succeeding
Blaire walked around her garden in the morning and saw that 18 of her tomato plants had tomatoes ready to pick. If this was 90% of her tomato plants, how many tomato plants does Blaire have altogether?
Blaire has 20 tomato plants altogether.
Step-by-step explanation:
Given,
Tomatoes plants ready to pick = 18
This represents 90% of total tomato plants.
Let,
x be the original number of tomato plants.
90% of x = 18
[tex]\frac{90}{100}*x=18[/tex]
[tex]0.9x=18[/tex]
Dividing both sides by 0.9
[tex]\frac{0.9x}{0.9}=\frac{18}{0.9}[/tex]
[tex]x=20[/tex]
Blaire has 20 tomato plants altogether.
Keywords: percentage, division
Learn more about division at:
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